What is (q/r+1)/(r/q-1) ?

The solution to (q/r+1)/(r/q-1) is ((r+q)q)/(r(-q+r))

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simplify (q/r+1)/(r/q-1)

simplify

\frac{\frac{q}{r} + 1}{\frac{r}{q} - 1}

\frac{( r + q ) q}{r ( - q + r )}

Solution steps

\frac{\frac{q}{r} + 1}{\frac{r}{q} - 1}

Join

\frac{q}{r} + 1 : \frac{r + q}{r}

= \frac{\frac{r + q}{r}}{\frac{r}{q} - 1}

Join

\frac{r}{q} - 1 : \frac{- q + r}{q}

= \frac{\frac{r + q}{r}}{\frac{- q + r}{q}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( r + q ) q}{r ( - q + r )}

\frac{( - 3 x ^{- 4} y ) ^{- 4}}{( 5 x ^{- 2} y ^{3} ) ^{0}}

5 x^{2} - 10 x - 5

ln (5 x) + ln (3 x) > 9

2 x^{2} + 6 x = 1

2 x^{2} + x - 6 \geq 0